Proofs of definability of some varieties and sets of varieties of semigroups

TL;DR

This paper demonstrates that many significant varieties and collections of semigroup varieties can be characterized by simple first-order formulas within the lattice of all semigroup varieties.

Contribution

It provides new definability results for varieties and sets of varieties of semigroups using straightforward first-order formulas.

Findings

Many important varieties are definable by simple formulas

Sets of varieties can be characterized within the lattice structure

The approach simplifies understanding of the lattice of semigroup varieties

Abstract

We show that many important varieties and sets of varieties of semigroups may be defined by relatively simple and transparent first-order formulas in the lattice of all semigroup varieties.